It depends on the chord for me. Can you give an example of a chord you are trying to mute with the thumb.
I just grabbed an acoustic with a fairly wide neck and was able to mute the low E with the thumb while playing an A minor.
My glove size is a medium, so I don't have particulary long fingers.
It could be hand size, technique or flexibility. Technique and flexibility will both improve over time just through regular practice.
Hendrix used the thumb a lot, and when I am trying to play some of the chords he played, there is just no way I can do it.
edited
This year the diet is definitely gonna stick!
